Aircraft: B757
Phase of flight: Initial Approach
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Weather / Turbulence

The flight had been uneventful and we were descending for the ILS Z 04R into ZZZZ. As we passed approximately 6;000 feet for 4;000 feet; Approach Control told us that an aircraft had just executed a missed approach into ZZZZ. A couple of minutes later he said a second aircraft had executed a missed approach as well. We asked for the reasons for the missed approaches and an update on the weather. The second aircraft gave us an update saying the weather was below 100 feet and he had never had a visual on the runway. Approach then said the weather had dropped to below 100 feet ceiling and asked for our intentions. We told him we needed to hold and were cleared to hold at XXXXX as published. We entered the hold and checked our alternate on the flight plan which was ZZZZ1 and knew that wouldn't work. We checked the weather again at destination and it was still reporting 700 broken but Approach Control was saying that it was actually still below 100 feet. We discussed our divert options and initially came up with ZZZZ2; ZZZZ3; and ZZZZ4. Our fuel was now at 7.1 and we decided that we didn't feel we had the gas to attempt the approach at destination and then divert without going emergency fuel so we opted to divert to ZZZZ4 due to being the most familiar with it; it would have company personnel; long runways with Cat II and III approaches if the weather went bad there as well. It and ZZZZ2 were about equal distances away. We informed Approach Control of our intentions and he told us he would coordinate it. We began setting up the FMS and the Relief Pilot was sending the Dispatcher our intentions. We initially were cleared to climb to FL170 and turn to XXX (VOR). From there we were cleared to XXY (VOR) and the ILS 16R approach into ZZZZ3. Approximately 30 miles from XXX we received an ACARS from the Dispatcher that ZZZZ3 was not listed as a 757 alternate. Our fuel was now 5.8 as we were still climbing through approximately 14;000 feet to FL210. Our FMS showed us landing in ZZZZ3 with about 3.8 in fuel and with the additional distance now to ZZZZ2 or ZZZZ4 we opted to continue to ZZZZ3. I had made a bad assumption that because ZZZZ3 was a major airport we flew into with 767 that the 757 was OK as well. We hadn't checked the divert airport chart and had now backed ourselves into a corner where we felt it would be more unsafe to switch diverts than to proceed. The approach and landing into ZZZZ3 were briefed and flown without problems (actual landing fuel was 4.5); and we were taxied to a remote pad to be refueled and redispatched. That's when we learned one of the reasons ZZZZ3 is not a 757 alternate is the company does not have the numbers for a 757 dispatch from there. We ended up causing a lot of extra work for the Dispatcher and the ground crew in ZZZZ3 who did an excellent job in working through all the problems keeping the passengers informed of what we and they were doing; and the Dispatcher who was working everything from his end. A B757 flight crew diverted from ZZZZ to ZZZZ3 due to weather and fuel remaining. While enroute they learned their diversion airport was not an approved alternate although it was for company B767's. Due to fuel remaining they continued and landed under the Captain's command authority.